FM stereo demodulation techniques, having been developed in the 1930s, are well known in the art. The signal transmitted over the air is referred as the FM stereo MPX signal. A diagram illustrating the spectral components of a conventional FM stereo MPX signal is shown in FIG. 1. A stereo signal is constructed at the FM transmitter by taking the sum and difference of the left (L) and right (R) channels and transmitting both along with a pilot carrier. The sum signal is referred to as the mono component and the difference signal is referred to as the stereo component. The mono component is sent baseband while the stereo component is modulated by a 38 kHz stereo carrier that is suppressed in the transmitted signal. The final spectrum, generally referenced 10, thus comprises a baseband mono signal portion 12 (i.e. L+R) for compatibility with radios not able to decode the stereo signal, a 19 kHz pilot carrier tone 14, a stereo signal portion 16 (L−R), centered at 38 kHz, that must first be decoded at the receiver and an optional Radio Data System (RDS) signal 18 centered at 57 kHz.
Prior art FM stereo demodulation is achieved by extracting two audio signal paths from the MPX (FM stereo) signal. The demodulation is assisted by the FM stereo indication pilot carrier 16 located at 19 kHz. A stereo decoder takes the demodulated signal and regenerates the stereo component carrier using a phased locked loop (PLL) locked on the pilot tone. It then uses this carrier for demodulation of the stereo audio component (i.e. L−R signal).
A block diagram illustrating an example prior art stereo decoder circuit is shown in FIG. 2. The stereo decoder, generally referenced 20, comprises a phase locked loop 22, mixer 26, stereo signal path low pass filter 28, mono signal path low pass filter 32, summer 30 and difference block 34. The pilot recovery PLL 22 comprises a multiplier 23, low pass filter 25, loop filter 27, voltage controller oscillator (VCO)/numerically controlled oscillator (NCO) 29 and divided by two block 31.
In operation, the MPX stereo signal is input to two paths: a stereo path and a mono path. In the mono path, the MPX signal is simply low pass filtered by LPF 32 which functions to pass the M=L+R mono signal component. In the stereo path, the MPX signal is input to the pilot recovery PLL which functions to recover the stereo carrier from the 19 kHz pilot tone. The MPX signal is multiplied by the quadrature of the recovered pilot tone via multiplier 23. The product then undergoes low pass filtering via LPF 25. This operation generates a signal proportional to the phase error between the reconstructed pilot carrier and the MPX pilot signal. This phase error signal then undergoes loop filtering via loop filter 27 in order to achieve smoothing of unwanted transients. The output of the loop filter is the frequency deviation input to the VCO block 29. The output of the VCO block is the regenerated stereo carrier used to demodulate the stereo signal. The frequency of the recovered stereo carrier signal is also divided by 2 via block 31 and is used to close the loop.
The 38 kHz pilot tone output of the VCO is multiplied with the MPX signal via multiplier 26. The resulting product is then low pass filtered via LPF 28 which functions to pass the S=L−R stereo signal component. The sum and difference of the S and M signals are then generated via summer 30 and difference block 34 to yield the left and right audio channels, respectively.
As described above, a conventional stereo FM radio signal contains a pilot carrier that is used to reconstruct the stereo carrier (which was suppressed at the transmitter) which is then used to modulate the stereo component of the FM signal. The stereo channel separation performance of a stereo FM receiver is limited by the phase accuracy of the reconstructed stereo carrier signal. The stereo carrier phase inaccuracy is expressed as the phase offset between the recovered pilot carrier and the actual true stereo carrier. The phase offset is typically caused by non-idealities at both the transmitter and the receiver. Thus, if there is a phase (i.e. angle) difference between the phase of the transmitted pilot and the stereo pilot used to modulate the stereo component, the full stereo S signal cannot be generated at the receiver. Ideally, the phase difference is zero which permits high stereo separation between L and R channels since the full amplitude of S can be generated. In reality, however, this is not possible.
The stereo FM modulation standard ITU-R recommendation BS.450-3, “Transmission standards for FM sound broadcasting at VHF,” ITU, 1982-1995-2001, allows for a phase inaccuracy in the stereo pilot of up to 3 degrees. Such a phase offset will cause a phase offset of up to 6 degrees on the stereo component carrier, whose frequency is twice that of the pilot frequency. In practice, however, numerous commercial FM broadcast stations exhibit an even greater phase offset then 3 degrees between the stereo indication pilot and the stereo component carrier.
Such a phase offset limits the amount of stereo channel separation the MPX decoder is able to achieve when using the classical phased locked loop (PLL) to recover the stereo carrier from the transmitted pilot wave. The problem is expressed mathematically below.
Consider a transmitted signal y(t):y(t)=M(t)+sin (ωt+Δθ)+S(t) sin (2ωt)  (1)where                M(t) is the mono component (i.e. Left+Right audio)        S(t) is the stereo component (i.e. Left−Right audio)        ωt is the stereo indication pilot phase (i.e. 19 kHz)If the pilot recovery PLL completely restores the pilot phase, the estimated stereo component will be as follows:Sest(t)=LPF·{y(t) sin (2ωt+2Δθ)}  (2)where        LPF is the output of the low pass filter applied to filter out the higher frequency components created by mixing down the stereo component.Further analysis yields:        
                                                                                          y                  ⁡                                      (                    t                    )                                                  ⁢                                  sin                  ⁡                                      (                                                                  2                        ⁢                        ω                        ⁢                                                                                                  ⁢                        t                                            +                                              2                        ⁢                        Δθ                                                              )                                                              =                            ⁢                                                                    M                    ⁡                                          (                      t                      )                                                        ⁢                                      sin                    ⁡                                          (                                                                        2                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                +                                                  2                          ⁢                          Δθ                                                                    )                                                                      +                                                                                                      ⁢                                                                    sin                    ⁡                                          (                                                                        ω                          ⁢                                                                                                          ⁢                          t                                                +                        Δθ                                            )                                                        ⁢                                      sin                    ⁡                                          (                                                                        2                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                +                                                  2                          ⁢                          Δθ                                                                    )                                                                      +                                                                                                      ⁢                                                S                  ⁡                                      (                    t                    )                                                  ⁢                                  sin                  ⁡                                      (                                          2                      ⁢                      ω                      ⁢                                                                                          ⁢                      t                                        )                                                  ⁢                                  sin                  ⁡                                      (                                                                  2                        ⁢                        ω                        ⁢                                                                                                  ⁢                        t                                            +                                              2                        ⁢                        Δθ                                                              )                                                                                                                          =                            ⁢                                                                    M                    ⁡                                          (                      t                      )                                                        ⁢                                      sin                    ⁡                                          (                                                                        2                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                +                                                  2                          ⁢                          Δθ                                                                    )                                                                      +                                                                                                      ⁢                                                sin                  ⁢                                      (                                                                  ω                        ⁢                                                                                                  ⁢                        t                                            +                      Δθ                                        )                                    ⁢                                      sin                    ⁡                                          (                                                                        2                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                +                                                  2                          ⁢                          Δθ                                                                    )                                                                      +                                                                                                      ⁢                                                                    1                    2                                    ⁢                                      S                    ⁡                                          (                      t                      )                                                        ⁢                                      cos                    ⁡                                          (                                              2                        ⁢                        Δθ                                            )                                                                      +                                                      1                    2                                    ⁢                                      S                    ⁡                                          (                      t                      )                                                        ⁢                                      cos                    ⁡                                          (                                                                        4                          ⁢                          ω                          ⁢                                                                                                          ⁢                          t                                                +                                                  2                          ⁢                          Δθ                                                                    )                                                                                                                              (        3        )            The signal is passed through a low pass filter which leaves only the ‘baseband’ components, as follows:
                                          S            est                    ⁡                      (            t            )                          =                                            1              2                        ⁢                          S              ⁡                              (                t                )                                      ⁢                          cos              ⁡                              (                                  2                  ⁢                  Δθ                                )                                              ≈                                    1              2                        ⁢                          S              ⁡                              (                t                )                                      ⁢                          (                              1                -                                                                            (                                              2                        ⁢                        Δθ                                            )                                        2                                    2                                            )                                                          (        4        )            
The ITU cited supra defines stereo separation as the following. First, an audio signal is transmitted on the Left audio channel only. Then, the relation between the desired signal received on the Left channel to the signal leakage on the Right channel is the stereo separation.
Thus, in this example, we have:M(t)=S(t)=L  (5)The desired signal at the Left channel will be:
                                                        L              =                            ⁢                                                1                  2                                ⁢                                  (                                                            M                      ⁡                                              (                        t                        )                                                              +                                          2                      ·                                                                        S                          est                                                ⁡                                                  (                          t                          )                                                                                                      )                                                                                                        ≈                            ⁢                                                1                  2                                ⁢                                  M                  ⁡                                      (                    t                    )                                                  ⁢                                  (                                      1                    +                    1                    -                                                                                            (                                                      2                            ⁢                            Δθ                                                    )                                                2                                            2                                                        )                                                                                                        ≈                            ⁢                              M                ⁡                                  (                  t                  )                                                                                        (        6        )            Similarly, the leakage signal on the Right channel will be:
                                                        R              =                            ⁢                                                1                  2                                ⁢                                  (                                                            M                      ⁡                                              (                        T                        )                                                              -                                          2                      ·                                                                        S                          est                                                ⁡                                                  (                          t                          )                                                                                                      )                                                                                                        ≈                            ⁢                                                1                  2                                ⁢                                  M                  ⁡                                      (                    t                    )                                                  ⁢                                  (                                      1                    -                    1                    +                                                                                            (                                                      2                            ⁢                            Δθ                                                    )                                                2                                            2                                                        )                                                                                                        ≈                            ⁢                                                1                  4                                ⁢                                  M                  ⁡                                      (                    t                    )                                                  ⁢                                                      (                                          2                      ⁢                      Δθ                                        )                                    2                                                                                                        =                            ⁢                                                M                  ⁡                                      (                    t                    )                                                  ⁢                                                      (                    Δθ                    )                                    2                                                                                        (        7        )            The total stereo separation is therefore limited by:
                    MaxSeparation        <                  20          ⁢                                    log              10                        ⁡                          (                              L                R                            )                                      ≈                  40          ⁢                                    log              10                        ⁡                          (              Δθ              )                                                          (        8        )            Thus, for example, for a phase offset of 3 degrees the stereo separation is limited to 51 dB. A phase offset of just 15 degrees, however, limits the separation to only 23 dB.
Note that the use of narrow-band loop filters in the receiver PLL to improve the total stereo audio quality raises the maximum possible instantaneous phase offset. Note also that most FM radio manufactures assume an ideal transmitted signal and attempt to improve the pilot recovery at the receiver. This, however, is not the case as the ITU allows for a small phase offset, thus leading to lower stereo separation.
There is thus a need for a mechanism that overcomes the disadvantages of the prior art. In particular, there is a need for a FM stereo decoder that is able to improve the stereo separation in an FM stereo radio without degrading the performance of the radio and without significantly increasing the cost and complexity of the radio.